The Heisenberg limit of quantum measurement where the measurement precision scales as N-1 with the number of atoms N can be achieved by introducing quantum correlations between the atoms. In the present work, we show how to reach Heisenberg scaling by implementing a new Ramsey measurement scheme for cold-atom metrological devices. The proposed protocol consists of a sequence of one-axis twisting pulses and total collective spin rotations. It results in the creation of atomic Schrödinger-cat states, a superposition of two coherent spin states. Analyzing the Fisher information, we discuss the main features of the states and their interferometric precision.
We present an analysis of the robustness of existing analytic schemes for the implementation of an atomic fountain interferometer, and develop concepts for improving this robustness through the use of optimal control theory. For an interferometer operating in the Raman regime, we consider an implementation that manipulates the atomic momentum states with a series of Rabi pulses, and analyze how robust the population dynamics are with respect to variations in the effective pulse amplitude seen by the atoms in the atomic clouds, and variations in the initial velocity of the atoms relative to the rest frame. We then show that using rapid adiabatic passage to implement momentum transfer can significantly improve this robustness. Finally, we formulate the most general control conditions for an atomic fountain interferometer and design a functional that can be used for an ensemble optimization over the robustness landscape. We show preliminary results of optimizing the system using Krotov's method, suggesting that optimal control may be able to significantly enhance the robustness of atom interferometers.
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